Protonation equilibria studies of quercetin in aqueous solutions of ethanol and dimethyl sulphoxide

Journal of Molecular Liquids 224 (2016) 1227–1232

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Protonation equilibria studies of quercetin in aqueous solutions of ethanol and dimethyl sulphoxide Rahil Yazdanshenas, Farrokh Gharib ⁎ Chemistry Department, Shahid Beheshti University, G. C., Tehran, Evin, Iran

a r t i c l e

i n f o

Article history: Received 8 August 2016 Received in revised form 21 October 2016 Accepted 21 October 2016 Available online 24 October 2016 Keywords: Quercetin Protonation constant Solvent effect Dielectric constant Kamlet-Abboud-Taft parameters

a b s t r a c t The protonation constants of quercetin were determined in different aqueous solutions of ethanol and dimethyl sulphoxide using a combination of potentiometric and spectrophotometric methods at constant temperature (25.0 °C) and ionic strength (0.1 mol dm−3 NaCl). It has been shown that the protonation constants of quercetin increases with increasing proportion of the both organic solvents in the binary mixtures. The protonation constants were analyzed using dielectric constant and Kamlet, Abboud, and Taft (KAT) parameters. A linear correlation of log K versus the reverse dielectric constant was obtained in the different aqueous organic solvents solutions. Dual-parameter correlation of log K versus α (hydrogen bond donor acidity) and π* (dipolarity/polarizability) parameters gave good results in the different binary aqueous solutions of the organic solvents. Three different extrapolation procedures including mole fraction, reversed dielectric constant, and Yasuda-Shedlovsky plots were used to determine the protonation constants of quercetin at zero percent organic solvent. Finally, the results were discussed in terms of the effect of organic solvent on protonation equilibria. © 2016 Elsevier B.V. All rights reserved.

1. Introduction Although, water is considered as the best solvent to represent almost all physiological conditions of drugs, but many compounds especially those have lower polarities are insoluble or at least sparingly soluble in water. In a variety of chemical fields such as chemical synthesis, solvent extraction, liquid chromatography, etc., mixtures of water and organic solvents are used. Aqueous organic solutions commonly methanol or ethanol (as protic solvents) and acetonitrile, dimethyl sulphoxide, or dioxane (as aprotic solvents) have been widely used due to the low solubility of many materials in pure water. Further, any physicochemical property of solutions can be easily changed by changing the compositions of water or organic solvents in the mixture. Previously, the solvent effect on protonation equilibria was believed to be guided chiefly by electrostatic interactions (Born model [1]). However, recent studies have revealed that the change in macroscopic properties such as the dielectric constant of the solvent cannot be the sole factor [2]. It is desirable to develop other empirical functions to take into account the complete picture of all intermolecular forces acting between solute-solvent as well as solvent-solvent molecules (see hereafter). ⁎ Corresponding author. E-mail address: [email protected] (F. Gharib).

http://dx.doi.org/10.1016/j.molliq.2016.10.108 0167-7322/© 2016 Elsevier B.V. All rights reserved.

Flavonoids are one of the largest groups of polyphenolic compounds, almost in all plant tissues, and play key roles in a wide range of biological processes [3–4]. It is well known that flavonoids are effective scavengers of radicals and thereby capable of an antioxidant effect. The diets rich in fruit and vegetables are protective against cardiovascular and neurodegeneration diseases as well certain forms of cancer [5–6]. The action mechanism of flavonoids as antioxidant is not fully known, but it is accepted the hydroxyl groups and chemical structures have vital roles in their free radical scavenging. Up to now, three mechanisms have been accepted for the free radical scavenging ability of these compounds [7–10]. These are mostly dependent on the chelating capacity of flavonoids and largely on the number, position, and dissociation of their hydroxyl groups [11–14]. Therefore, the acidity constant is an important parameter controlling the antioxidant capacity of flavonoids. Further, the acidity constant of flavonoids can explain the influence of pH changes in solubility, membrane permeability, and reactivity of different forms of flavonoids in biological processes [15–17]. In the present work, the protonation constants of quercetin have been determined in different aqueous solutions of ethanol (as an amphiprotic solvent) and dimethyl sulphoxide, DMSO, (as a dipolar aprotic solvent) at 25.0 °C and ionic strength 0.1 mol dm−3 NaCl. The dependences of the acid-base equilibria on the binary solvent mixtures with different compositions and various polarities were determined and analyzed using solvent polarity and KAT parameters. Also, the

R. Yazdanshenas, F. Gharib / Journal of Molecular Liquids 224 (2016) 1227–1232

protonation constants of quercetin were calculated using YasudaShedlovsky extrapolation method to zero percent ethanol. 2. Experimental 2.1. Materials Quercetin (3, 5, 7, 3′, 4′-pentahydroxy-flavone), Scheme 1, was obtained from Sigma-Aldrich as analytical reagent grade material. Hydrochloric acid and sodium hydroxide solutions (Merck), prepared from concentrated ampoules, were standardized against sodium carbonate and potassium hydrogen phthalate, respectively. Sodium chloride solutions were prepared by weighing the pure salt (Merck) previously dried in an oven at 110 °C for 2 h. Ethanol and DMSO (reagent grades) were from Merck and used without further purification. All dilute solutions were prepared from double-distilled water with a conductance equal to 1.2 ± 0.1 μS. 2.2. Procedure and measurements The electromotive force was measured using a Jenway research pHmeter model 3420, equipped with a combined glass-pH electrode (Jenway model). The electrode response can read to the third decimal place in terms of pH units with a precision of ± 0.001 and potential with a precision of ±0.1 mV. All titrations were carried out in a 30 mL thermostated double-walled glass vessel and the test solution was stirred magnetically. To exclude any atmospheric oxygen and carbon dioxide from the system, a stream of purified nitrogen was passed through a sodium hydroxide solution and then bubbled slowly through the reaction solution. Spectrophotometric measurements were performed on a UV–Vis Shimadzu 2100 spectrophotometer (350 to 450 nm in the interval of 0.5 nm) equipped with a computer and using thermostated matched 10 mm quartz cells. Before the spectrophotometric-potentiometric measurement, the system calibration was performed according to the Gran's method [18]. For this purpose, a measured amount of an acidic solution (20.0 mL 0.01 mol mol−3 HCl) was placed in the double-wall glass vessel. The electrode was immersed in the solution in the thermostated vessel and the acidic solution was then titrated potentiometrically with a strong base (0.1 mol mol− 3 NaOH) both with the same ionic strength (0.1 mol dm− 3 NaCl) and the organic solvent compositions (30–70 and 30–60% v/v ethanol and DMSO, respectively) to be used in later experiments at 25.0 °C. The potential was allowed to stabilize after each addition of the titrant (0.05 mL) and the recorded emf values were then used to obtain the cell parameter (E°) and the electrode calibration slope, Nernstian parameter, k, as was described in detail in our previous compilations [19–20]. The procedure was continued to pH ≅ 2.5. Usually, 10 to 12 additions are enough for this purpose. The recorded emf values were then converted to pCH (−log [H+]) using the method described in the literature [21].

One of the main obstacles in studying protonation constants of quercetin (or some other flavonoids) in solution is its facile oxidation by air oxygen, especially in strongly basic solutions [22–24], which causes a change in optical density and consequently an error in calculations. This means the usual potentiometric-spectrophotometric titration method cannot be used to determine the protonation constants of quercetin. Although, the life time of quercetin is reported longer in aprotic solvents like acetonitrile compared with those in protic solvents such as methanol [25], our obtained results have shown that: (1) quercetin is stable in acidic solution, (2) between pH ≅ 7–11 the stability time is around 15 min, (3) more than this pH the stability is only for a short time. So, the following procedure has been used. 100 mL of an acidic stock solution (0.01 mol dm− 3 HCl) of quercetin [(1.0– 2.0) × 10−4 mol dm−3] was prepared in the desired percent of ethanol or DMSO. In a series of 10-mL volumetric flasks, 2.0 mL of the stock solution of quercetin (freshly prepared), 1.0 mL sodium chloride solution (1.0 mol dm− 3), sodium hydroxide solution (0.1 mol dm− 3) in the order of 0.0, 0.1, 0.2, …, and 2.0 mL, and finally sufficient ethanol, DMSO, or water was added to the respective flasks (to maintain 30– 70% v/v ethanol or 30–60% v/v DMSO). Unfortunately, it was impossible to maintain higher percentages of DMSO in solution owing to limited solubility of the background electrolyte. The mixtures were sonicated (2 min) to form a clear and homogenous solution. The emf and absorption spectra of each solution were recorded immediately after achieving the desired temperature. At least two replicate measurements were made for each solution. 3. Results and discussion There are two major absorption maxima in the UV–Vis spectrum of quercetin [26–27]. The first absorption maximum, band II, appears in the range of 350–400 nm which is referred to π → π* transitions in the A ring whereas the second absorption maximum, band 1, between 1.2

HO

O 7

A

C

5

4

OH

0.8 0.6 0.4

0.0 260

280

300

320

340

360

380

400

1.8

b

1.6

440

pCH 7.2 8.3 9.1 9.2 10.1 11.0

1.4

OH

420

Wavelength (nm)

Absorbance

B

pCH 2.2 2.3 2.5 2.7 2.9 3.1 3.4

0.2

OH 3' 4 '

a

1.0

Absorbance

1228

1.2 1.0 0.8 0.6 0.4 0.2

3

OH

O

Scheme 1. Chemical structure of quercetin.

0.0 280

300

320

340

360

380

400

420

440

Wavelength (nm) Fig. 1. Absorption spectra of quercetin solution at different pCH, (a) in acidic (b) in basic media.

R. Yazdanshenas, F. Gharib / Journal of Molecular Liquids 224 (2016) 1227–1232

h

H5−n Ln− þ Hþ ⇆H6−n L1−n

i H6−n L1‐n   Kn ¼  H5−n Ln− Hþ

ð1Þ

where H5L represents the full protonated quercetin, n is the number of proton accepted at each step, and Kn shows the protonation constant. The protonation constants determined at constant temperature (25.0 °C), constant ionic strength (0.1 mol dm−3 NaCl), and different aqueous solutions of ethanol and DMSO. The protonation constants of quercetin determined spectrophotometrically based on the relation A = f(pCH) [33]. The measured absorbance, A, (350–450 nm in the interval of 0.5 nm) and pCH were used with the computer program Squad [34–35]. The data in the computer program were fitted to Eq. (1) by minimizing the error square sum of the difference in the experimental absorbances and the calculated ones. The program allows calculation of the protonation constants with different stoichiometries. The resulted protonation constant values of quercetin (in log scale) in different aqueous solutions of ethanol and DMSO are listed in Table 1 together with some values reported in the literature for comparison [24,31,36]. With small differences, the protonation constant values obtained in this work are in agreement with those reported before. The differences are possibly due to the different experimental method and the different background electrolyte used. In Fig. 2, the species mole fractions of quercetin in different pCH are shown in 30% ethanol. It is known that a solvent with low dielectric constant increases the electrostatic forces between the ions and facilitates formation of molecular species [2]. Indeed, as the dielectric constant of the medium decreases, the ion interaction involving the proton and the anionic oxygen of the hydroxyl group decreases to a greater extent than the ion dipole interaction between the proton and the solvent molecule.

Table 1 Protonation constants of quercetin at 25.0 °C, 0.1 mol dm−3 NaCl, and different aqueous solutions of ethanol and DMSO, together with some values reported in the literature for comparison.a Organic solvent (% v/v)

Ethanol log K1

log K2

log K3

log K1

log K2

log K3

30 35 40 45 50 55 60 65 70 0.0 0.0 0.0

7.93 7.98 8.04 8.11 8.17 8.25 8.34 8.45 8.61 6.41b 6.60c 7.10d

9.36 9.37 9.39 9.42 9.44 9.47 9.49 9.51 9.54 7.81b 8.10c 9.09d

10.22 10.25 10.28 10.32 10.36 10.41 10.46 10.51 10.58 10.19b – 11.12d

8.07 8.08 8.09 8.10 8.11 8.12 8.14 – –

9.75 9.76 9.77 9.79 9.80 9.83 9.85 – –

10.34 10.34 10.35 10.36 10.38 10.40 10.42 – –

a b c d

DMSO

The uncertainties in the log K values are 0.05 or lower. The values at 0% organic solvent, taken from Ref. [24]. The values at 0% organic solvent, taken from Ref. [31]. The values at 0% organic solvent, taken from Ref. [36].

So, in general, decreasing the dielectric constant of the medium causes an increase in protonation constant value which is consistent with the present results, Table 1. Also, there is a variation in the number of charges between the reactants and products species in Eq. (1), so the protonation constant should depend on the dielectric constant of the medium. The correlation between the protonation constants of quercetin (in log scale) and the reverse of the dielectric constants of the aqueous solutions of ethanol and DMSO are shown below using the computer program Linest [37]: log K 1 ðethanolÞ ¼ 5:03ð0:08Þ þ 213:86ð5:85Þε −1 N ¼ 9; R2 ¼ 0:99

ð2Þ

log K 2 ðethanolÞ ¼ 8:57ð0:08Þ þ 58:91ð5:09Þε−1 N ¼ 9; R2 ¼ 0:95

ð3Þ

log K 3 ðethanolÞ ¼ 8:66ð0:09Þ þ 115:59ð5:77Þε −1 N ¼ 9; R2 ¼ 0:98

ð4Þ

log K 1 ðDMSOÞ ¼ 2:19ð0:28Þ þ 463:00ð21:88Þε−1 N ¼ 7; R2 ¼ 0:98

ð5Þ

log K 2 ðDMSOÞ ¼ 0:84ð0:70Þ þ 701:08ð54:51Þε−1 N ¼ 7; R2 ¼ 0:96

ð6Þ

log K 3 ðDMSOÞ ¼ 2:94ð0:86Þ þ 581:57ð67:02Þε−1 N ¼ 7; R2 ¼ 0:93

ð7Þ

1.0 species mole fraction

280 and 320 nm is attributed to transitions in the B ring, Fig. 1. When NaOH solution was added to the acidic solution of quercetin, the light yellow color changes gradually to dark yellow and the absorption band II progressively decreases to a lower value. Deprotonation of quercetin has been shown to induce a dramatic change in absorption values from band II to I. Finally, the absorption values of band I increase to higher values at higher pH, Fig. 1. It is worthy to note that the phenomenon was reversed by increasing the acidity of the medium. Similar behaviors were observed for almost all other flavonoids [27–30], suggesting that these moieties are responsible with metal ion chelation [26]. Considering Scheme 1, there are five ionizable OH groups in quercetin with protonation constant relatively close to each other. The determination of all protonation constants is a difficult task, because at least two of them occur at very high pH values [24]. Recently, it is reported that at low pH values, protonation of carbonyl oxygen atom of the flavonoid can be occurred and the corresponding protonation constant was determined (log K = 1.8) [31]. Several methods including spectrophotometry and potentiometry have been used to determine the protonation constants of quercetin and the resulted values by different researchers are summarized from the year 1954 to 2008 [32]. But, large differences can be seen between these values, in some cases it exceeds to about 4 pKa units. This is possibly due to the high oxidizability of quercetin especially in alkaline solutions. In this study a wide pH range is considered, 2.0–11.0, but this range does not cover to determine the fourth and the fifth protonation constants of quercetin. So, the fourth and the fifth protonation constants of quercetin are not considered in this study. Quercetin, shown in Scheme 1, may donate five protons from its hydroxyl groups. Using a computational approach [24], it has been specified that the first proton is released from the hydroxyl group at the site 4′ around the neutral pH and the others from 7, 3, 3′, respectively, and finally the fifth one from the site 5 at a very alkaline pH. These are referred to the following equilibria, Eq. (1):

1229

H5 L

0.8

H 4L-

H 2L3H 3 L2-

0.6 0.4 0.2 0.0

4.0

6.0

8.0 pCH

10.0

12.0

Fig. 2. Distribution diagram of the different quercetin species at 25.0 °C and 30% v/v ethanol.

1230

R. Yazdanshenas, F. Gharib / Journal of Molecular Liquids 224 (2016) 1227–1232

Table 2 Mole fractions, X, KAT parameters, and the dielectric constants, ε, of different aqueous solutions of ethanol and DMSO. Organic solvent Ethanol (% v/v) X εa

αb

βc

π*b

X

εd

αb

βc

π*b

0 30 35 40 45 50 55 60 65 70

1.17 1.07 1.05 1.02 1.00 0.98 0.97 0.96 0.95 0.96

0.47 0.49 0.52 0.55 0.58 0.61 0.64 0.66 0.67 0.66

1.09 1.16 1.15 1.13 1.10 1.06 1.02 0.97 0.92 0.86

0.0 0.10 0.12 0.14 0.17 0.20 0.24 0.28

79.50 78.76 78.61 78.46 78.32 78.18 78.03 77.87

1.17 0.82 0.76 0.70 0.64 0.59 0.53 0.48

0.47 0.56 0.57 0.59 0.60 0.61 0.63 0.64

1.09 1.12 1.12 1.12 1.12 1.12 1.11 1.10

a b c d

0.0 0.12 0.14 0.17 0.20 0.24 0.27 0.32 0.37 0.42

79.50 73.18 72.14 71.03 69.82 68.44 66.83 64.88 62.46 59.45

DMSO

The values are taken from Ref. [44]. The values are taken from Ref. [42]. The values are taken from Ref. [43]. The values are taken from Ref. [45].

 2 S ¼ Σ log K exp – log K cal

where N and R2 are the number of different solutions and regression coefficient, respectively. Relatively good linear relationships are observed in Eq. (2–7), but it should be noted that this correlation considers only the electrostatic interactions measured by the dielectric constant and should be improved by taking into account the specific interactions caused by the solute and solvent molecules. In general, the Gibbs free energy of protonation equilibria consists of two terms: an electrostatic term, which can be estimated by the Born equation, and a nonelectrostatic term, which includes specific solute-solvent interactions [38]. When the electrostatic effects predominate, then in accordance with the Born equation, Eq. (8), the plot of log K versus the reciprocal of the dielectric constant of the media, ε, should be linear.   Δlog K ¼ 121:6Z 2 =r ð1=εsolution –1=εwater Þ

ð8Þ

where r is the common radius of the ions and Z2 is the square summation of the charges involved in the protonation equilibria. For example, Z2 = 2, 4, and 6 for the charge type H4L− ⇄ H5L, H3L2− ⇄ H4L−, and H2L3− ⇄ H3L2−, respectively. Considering the above discussion, the protonation constants of quercetin not only depend on solute-solvent interactions of different species in the mixtures but also are dependent to the polarity of the medium [39]. Therefore, it is necessary to elucidate the nature of solute-solvent interactions for a better understanding of solvent effects. From Table 1, it can be seen that Δlog K (log Kethanol-log KDMSO) values are increased by increasing the percentages of the organic solvents used. Also, it is worthy to note that the differences of log K from the highest to the lowest percentages of ethanol are much larger than the corresponding ones in DMSO. These are: 0.68, 0.18, and 0.36 for log K1, log K2, and log K3, respectively, in ethanol and 0.07, 0.10, and 0.08 in the case of DMSO. This is possibly due to the aprotic nature of DMSO. Solute-solvent interactions are caused by a multiple of non-specific (ion-dipole, dipole-dipole, dipole-induced dipole) and specific (hydrogen bonding, electron-pair donor-electron-pair acceptor interaction) as well as intermolecular forces between solute and solvent molecules. Therefore, it seems a multiparametric equation is needed to obtain a deeper insight into the solute-solvent interactions which influence the protonation constant. So, the multi-parametric approach according to LSER developed by Kamlet, Abboud, and Taft (KAT) was used [40–41]. The KAT equation, Eq. (9), contains specific as well as non-specific solute-solvent interactions separately. log K ¼ Ao þ aα þ bβ þ pπ

dipolarity/polarizability, respectively [2]. Indeed, α describes the ability of a solvent to donate a proton to a solute hydrogen-bond, β shows the ability of a solvent to accept a proton from a solute, and π* represents the ability of a solvent to stabilize a charge or a dipole by its own dielectric effects [2]. The regression coefficients a, b, and p measure the relative susceptibilities of the solvent dependence of log K to the solvent parameters. Ao is the regression value and represents log K in a hypothetical solvent for which α = β = π* = 0. In order to explain the log K values through the KAT solvent parameters, the protonation constants were correlated with the solvent properties by means of single, dual, and multiple regression analysis by a suitable computer program (Microsoft Excel Solver and Linest [37]). We used the Gauss-Newton non-linear least-squares method in the computer program to refine the log K by minimizing the error squares sum from Eq. (10).

ð9Þ

The solvatochromic parameters (α, β, and π*) represent solvent hydrogen-bond donor, solvent hydrogen-bond acceptor, and solvent

ð10Þ

The procedure used in the regression analysis involves a rigorous statistical treatment to find out which parameter in Eq. (9) is best suited to the water-organic mixed solvents. So, a stepwise procedure and least-squares analysis were applied to select the significant solvent properties to be influenced in the model and to obtain the final expression for the protonation constants. Therefore, the KAT equation, Eq. (9), was used as single, dual, and multi-parameters for correlation analysis of log K in the various solvent mixtures. The computer program used can gives the values of A0, a, b, p and some statistical parameters including R2 coefficient, uncertainty value of any parameter (given in bracket), the overall standard error (OSE), and total sums of squares (TSS) of log K. Although the solvent polarity is identified as the main reason of the variation of log K values in water-organic solvent mixtures, but the results show that any single-parameter correlation of log K values individually with π*, α, and β did not give good results in all cases. However, the correlation analysis of log K values (in the both solvent mixtures) with dual-parameter equations indicates significant improvement with regard to the single or multi-parameter models. The accepted expressions of the KAT equation for each property are obtained and are given as follows. log K 1 ðethanolÞ ¼ 10:41ð0:25Þ–0:38ð0:03Þα−2:09ð0:15Þπ ð11Þ N ¼ 9; R2 ¼ 0:994; OSE ¼ 2:07  10−2 ; TSS ¼ 2:57  10−3 log K 2 ðethanolÞ ¼ 10:33ð0:05Þ–0:43ð0:07Þα−0:44ð0:03Þπ ð12Þ N ¼ 9; R2 ¼ 0:997; OSE ¼ 4:04  10−3 ; TSS ¼ 9:78  10−5 log K 3 ðethanolÞ ¼ 11:77ð0:06Þ–0:33ð0:10Þα−1:02ð0:04Þπ ð13Þ N ¼ 9; R2 ¼ 0:999; OSE ¼ 5:32  10−3 ; TSS ¼ 1:70  10−4 log K 1 ðDMSOÞ ¼ 9:10ð0:27Þ–0:16ð0:01Þα−0:80ð0:25Þπ N ¼ 7; R2 ¼ 0:994; OSE ¼ 2:35  10−3 ; TSS ¼ 2:20  10−5

Table 3 Density of water-ethanol mixture values at 25.0 °C and 0.1 mol dm−3 NaCl. Ethanol (% v/v)

Density (g cm−3)a

0.0 30 35 40 45 50 55 60 65 70 100

0.99745 0.96378 0.95701 0.94817 0.93811 0.92840 0.91705 0.90594 0.89464 0.88171 0.78795

a The uncertainties in the density values are 0.00001 g cm−3 or lower.

ð14Þ

R. Yazdanshenas, F. Gharib / Journal of Molecular Liquids 224 (2016) 1227–1232

12.0

log K + log[H 2O]

using Anton Paar density-meter model DMA 4500 M with a precision of ±0.00001 g cm−3 unit and are listed in Table 3. The Yasuda-Shedlovsky equations are as follows:

K3

11.5 11.0

K2

10.5 10.0

K1

9.5 9.0 0.013

0.015

log K o 1 þ log½H2 O ¼ 8:58 þ 68:74ε−1

ð21Þ

log K o 2 þ log½H2 O ¼ 12:11−86:20ε −1

ð22Þ

log K o 3 þ log½H2 O ¼ 12:20–29:52ε −1

ð23Þ

Fig. 3 shows the Yasuda-Shedlovsky plots of the systems studied are linear with correlation coefficients more than 0.99. The log Ko values determined by the three different approaches are shown in Table 4. Data indicate that there are no appreciable differences between the three different extrapolation methods and the values are in agreement with each other.

0.017

ε -1 Fig. 3. The Yasuda-Shedlovsky plots in different aqueous solutions of ethanol.

log K 2 ðDMSOÞ ¼ 11:92ð0:42Þ–0:22ð0:02Þα−1:78ð0:38Þπ N ¼ 7; R2 ¼ 0:994; OSE ¼ 3:64  10−3 ; TSS ¼ 5:29  10−5

ð15Þ

log K 3 ðDMSOÞ ¼ 12:88ð0:33Þ–0:15ð0:02Þα−2:16ð0:31Þπ N ¼ 7; R2 ¼ 0:994; OSE ¼ 2:92  10−3 ; TSS ¼ 3:42  10−5

ð16Þ

This correlation analysis, Eq. (11–16), are much better than Eq. (2–7) and the polarity/polarizability parameter, π*, shows a major role in all cases (ca. 84.6, 50.6, 75.5, 83.3, 89.0, and 93.5% for log K1, log K2, and log K3 of ethanol and DMSO, respectively). Also, the negative signs of π* and α show that log K values (in both systems) should increase with decreasing the polarity and hydrogen-bond donor ability of the solvents. The KAT parameters and the dielectric constants for the binary mixtures used in this work were taken from the literature [42–45] and are listed in Table 2. In this work three different extrapolation methods have been used to obtain log Ko (at 0 % ethanol). First, the traditional plot of log K versus Xethanol (mole fraction of ethanol) was applied using the following equations. log K 1 ¼ 7:66 þ 2:19X ethanol

ð17Þ

log K 2 ¼ 9:29 þ 0:61X ethanol

ð18Þ

log K 3 ¼ 10:08 þ 1:19X ethanol

ð19Þ

The second extrapolation method is based on the linear relation between log K and the reverse dielectric constant of water-ethanol mixture, Eq. (2–4). The third method known as Yasuda-Shedlovsky extrapolation that establishes a correlation with the reverse dielectric constant of water-ethanol mixture but uses a modified equation, Eq. (20): log K þ log½H2 O ¼ a þ bε−1

1231

ð20Þ

where [H2O] is the molar water concentration of the given solvent mixture, as well a and b are two constants that should be determined for the different water-ethanol mixtures used in this work. This method is the most widely used procedure in cosolvent methods [46]. In this approach the density of all different solutions were determined at 25.0 °C

Table 4 log Ko (in pure water) values on the basis of (a) mole fraction of ethanol in the mixture, (b) the reverse dielectric constant of the aqueous ethanol solution, (c) Yasuda-Shedlovsky approach. The R2 values are also given for a better comparison. Different approaches

log Ko1

log Ko2

log Ko3

R21

R22

R23

a b c

7.66 7.72 7.70

9.29 9.31 9.28

10.08 10.11 10.09

0.996 0.995 0.994

0.988 0.950 0.998

0.989 0.983 0.996

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